The present invention relates to the determination of the time delay between at least two signals. The described techniques can also be applied generally to the determination of the amount by which a signal is shifted relative to another signal.
One obvious application of time-delay determination is the synchronisation of different processes or functions being performed in a complicated engineering system, especially a communication system. There are many other practical applications of time-delay determination; for example, radar and sonar systems. Also, in some industrial and biomedical applications, where a distance is known, but the velocity of a waveform, associated with some phenomenon or process, is required, this can be estimated by determining the time required for this phenomenon or process to travel the known distance.
One conventional method of determining a time delay xcex94t is to estimate the standard cross correlation function
Rxy(xcfx84)=(1/T)∫x(t).y(t+xcfx84)dt=(1/T)∫x(txe2x88x92xcfx84).y(t)dt
where the integral is evaluated over the observation interval of duration T and for a range of hypothesised time delays xcfx84min less than xcfx84 less than xcfx84max. The value of argument xcfx84, say xcfx840, that maximises the cross correlation function Rxy(xcfx84) provides an estimate of the unknown time delay xcex94t.
In general, the operation of cross correlation comprises the following three steps:
1. delaying the reference signal x(t) by xcfx84;
2. multiplying the values of a received signal y(t) and delayed reference x(t);
3. integrating the product obtained in step 2 over a specified observation time interval T.
A block diagram of a standard cross-correlator system is presented in FIG. 1. The system comprises a variable delay line 100, a multiplier 102 and an integrator 104. An example of a typical cross correlation curve, with its maximum determining the time-delay estimate xcfx840, is shown in FIG. 2.
The illustrated system performs the required operations and functions serially; however parallel systems are also known, in which for example the single variable delay line is replaced by a tapped (xe2x80x9cbucket-brigadexe2x80x9d-type) delay line, the taps providing incremental delays feeding respective multipliers whose outputs are fed to respective integrators.
It should be pointed out that the cross-correlation operation can be performed either in the time domain, as discussed above, or in the frequency domain.
The observed cross-correlation curve usually contains errors associated with random fluctuations in the signal itself as well as errors due to noise and interference effects. As a result, the task of locating the cross-correlation peak is rather difficult to carry out in practice. Even when the peak is well defined, its position is usually found by evaluating the cross-correlation function at several points and calculating corresponding differences to approximate the derivative of the cross correlation function. When this procedure is to be used in a tracking system, the additional operations required are computationally burdensome and inconvenient at best.
An important class of active methods for determining an unknown time delay is based on synchronous integration. FIG. 3 is a block diagram of an active system for determining time delay. The transmitted signal x(t) is delayed an unknown amount by signal path 300, and integrated by synchronous integrator 302 in synchronism with the transmitted signal x(t). The integration process in a synchronous integrator is initiated and controlled by a train of trigger pulses obtained by a trigger generator 304 from the signal x(t) itself. Known synchronous-integration systems employ repetitive composite signals which consist of a number of suitable identical waveforms. FIG. 4 shows an example of typical waveforms and operations performed by a synchronous integrator. In this case, each trigger pulse coincides with the leading edge of the signal waveform being transmitted. The output signal waveform y(t) is a time-delayed replica corrupted by noise and interference. If the total number K of integrated waveforms is sufficiently large, then the accumulated average, observed at the output of the synchronous integrator, will have the same shape as that of the repeatedly transmitted waveform x(t). The unknown time delay xcex94t can then be determined from the time difference between the occurrence of the trigger pulse and the leading edge of the accumulated average.
It would be desirable to provide an improved technique for determining time delay.
Aspects of the present invention are set out in the accompanying claims.
In a further aspect of the present invention, a time delay is measured between two signals, which correspond to each other but need not be identical. One of the signals is processed in order to determine a sequence of events which are separated by non-uniform intervals. The signal is preferably so designed that the events define an at least substantially aperiodic succession. Segments of the second signal are acquired at intervals corresponding to the intervals between the successive events derived from the first signal. The segments are combined. At a position within the combined segments which corresponds to the time shift between the first and second signals, the parts of the second signal which correspond to the events of the first signal will be combined together. This position can be determined from the combined segments. Accordingly, it is possible to determine that time shift which corresponds to the delay between the signals.
Preferably, the events are associated with edges of a binary signal, more preferably zero crossings of a bipolar signal so that the combined samples either average out to zero (if the time-shift does not correspond to the delay between the signals), or represent an odd function (if the time shift corresponds to the delay). By searching for the odd function, the correct delay time can be determined.
In preferred embodiments of the present invention described below a time-delay discriminator employs implicit sampling. Conventional signal processing techniques are based on observations obtained by sampling a signal of interest at predetermined (and generally equally-spaced) time instants (e.g., Nyquist sampling), independent of the values assumed by that signal (so-called explicit sampling). In contrast to explicit sampling, implicit methods of sampling make use of the time instants at which the signal of interest (or another signal associated with it) assumes some predetermined values.
In the preferred embodiments, the sequence of events is derived from a substantially aperiodic waveform, which may also be a chaotic waveform or other random or pseudo-random waveform, with suitable temporal characteristics. The waveform is utilised to produce a series of time marks, corresponding to the events, which can be regarded as a substantially random point process. Preferably, but not necessarily, these time marks are obtained by using suitably selected time instants at which the waveform crosses a predetermined constant level (for example zero level) or a level varying in time in some specified fashion. Zero-level crossings with positive slope will be referred to as zero upcrossings; similarly, zero-level crossings with negative slope will be referred to as zero downcrossings. Zero crossings (of real or complex waveforms) permit accurate and unambiguous representations of time instants.
The series of time marks obtained from the waveform is then utilised to construct a binary waveform in such a way that the time marks constitute the transition (switching) instants between two suitably selected voltage levels. Consequently, all relevant time information needed for time-delay determination will be encapsulated in the series of transition instants of the binary waveform. When a binary waveform is used, the potential additional uncertainty associated with the time-varying amplitude of a waveform is eliminated which results in more efficient and reliable time-delay determination. In particular, a symmetric (bipolar) binary waveform with random transition times may be regarded as a particularly desirable signal for the purpose of time-delay determination because its temporal structure is purely random, i.e. aperiodic and irregular, while its amplitude structure is very simple.
Such an arrangement is not however essential. It is important that the events, or time marks, occur at non-uniform intervals. These intervals could be integer multiples of a common period, e.g. a clock cycle, and indeed this may be likely in a digital system. The intervals need not, however, be wholly aperiodic; they could for example form a sequence which repeats (derived from a pseudo-random signal), but this is still substantially aperiodic so long as the repetition period is sufficiently long as to avoid ambiguous results (i.e. longer than the range of delays to be measured).
The invention may be embodied in an obstacle detection apparatus or other radar device, using for example a microwave carrier for transmitting one of the signals, and determining the delay between that signal and the received reflection.
Although a binary waveform constructed from a series of random time marks is used for time-delay determination, the random waveform actually employed for modulation of the carrier may in fact differ from this binary waveform because only time marks extracted from this random waveform are used. As a result, as long as the waveform can provide suitable time marks, its other parameters, e.g. those affecting its shape, may be chosen (or even xe2x80x98engineeredxe2x80x99) according to some other criteria, such as:
1. constant envelope (i.e. a continuous signal, such as a sine wave) for efficient power transmission;
2. a form suitable for modulation with reduced complexity;
3. noise-like appearance for low probability of interference.
It is preferred that the modulation of the carrier be such as to avoid corruption of the time information, such as might occur if, e.g., a simple pulse is transmitted at each time instant, and the transmission path is such that the amplitude rise time can be distorted.